Find the formula equal to 1 from the known conditions, and then multiply it by the required formula, and the value remains unchanged.

normal solution

y = 1/a+4/b =( 1/a+4/b)* 1

=( 1/a + 4/b)* [(a+b)/2]

= 1/2 *[ 1+b/a+4a/b+4]

= 1/2*[b/a+4a/b+5]

≥ 1/2 * [2 √ (b/a*4a/b)+5] ... Note that b/a * 4a/b is a fixed value here. 4. The conditions are met.

=9/2

When b/a=4a/b, we get an equal sign, a=2/3 and b=4/3.

Basic attribute

(1) if x>y, then y < x；; If y

2 If x>y, y & gtz；; Then x & gtz；; (transitivity).

③ if x>y and z is any real number or algebraic expression, then x+z >; y+z； (addition principle, or additivity of inequality in the same direction).

4 If x>y, z>0, then xz & gtyz；; If x>y, z<0, and then xz.

⑤ If x>y, m>n, then X+M > y+n； (Sufficiently unnecessary condition).